Solving iterated functions using genetic programming

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@InProceedings{DBLP:conf/gecco/SchmidtL09b,
  author =       "Michael D. Schmidt and Hod Lipson",
  title =        "Solving iterated functions using genetic programming",
  booktitle =    "GECCO-2009 Late-Breaking Papers",
  year =         "2009",
  editor =       "Anna I. Esparcia and Ying-ping Chen and 
                 Gabriela Ochoa and Ender Ozcan and Marc Schoenauer and Anne Auger and 
                 Hans-Georg Beyer and Nikolaus Hansen and 
                 Steffen Finck and Raymond Ros and Darrell Whitley and 
                 Garnett Wilson and Simon Harding and W. B. Langdon and 
                 Man Leung Wong and Laurence D. Merkle and Frank W. Moore and 
                 Sevan G. Ficici and William Rand and Rick Riolo and 
                 Nawwaf Kharma and William R. Buckley and Julian Miller and 
                 Kenneth Stanley and Jaume Bacardit and Will Browne and 
                 Jan Drugowitsch and Nicola Beume and Mike Preuss and 
                 Stephen L. Smith and Stefano Cagnoni and Jim DeLeo and 
                 Alexandru Floares and Aaron Baughman and 
                 Steven Gustafson and Maarten Keijzer and Arthur Kordon and 
                 Clare Bates Congdon and Laurence D. Merkle and 
                 Frank W. Moore",
  pages =        "2149--2154",
  address =      "Montreal",
  publisher =    "ACM",
  publisher_address = "New York, NY, USA",
  month =        "8-12 " # jul,
  organisation = "SigEvo",
  keywords =     "genetic algorithms, genetic programming",
  isbn13 =       "978-1-60558-325-9",
  bibsource =    "DBLP, http://dblp.uni-trier.de",
  DOI =          "doi:10.1145/1570256.1570292",
  size =         "5 pages",
  abstract =     "An iterated function f(x) is a function that when
                 composed with itself, produces a given expression
                 f(f(x))=g(x). Iterated functions are essential
                 constructs in fractal theory and dynamical systems, but
                 few analysis techniques exist for solving them
                 analytically. Here we propose using genetic programming
                 to find analytical solutions to iterated functions of
                 arbitrary form. We demonstrate this technique on the
                 notoriously hard iterated function problem of finding
                 f(x) such that f(f(x))=x2--2. While some analytical
                 techniques have been developed to find a specific
                 solution to problems of this form, we show that it can
                 be readily solved using genetic programming without
                 recourse to deep mathematical insight. We find a
                 previously unknown solution to this problem, suggesting
                 that genetic programming may be an essential tool for
                 finding solutions to arbitrary iterated functions.",
  notes =        "Bronze 2010 HUMIES GECCO 2010
                 http://www.genetic-programming.org/combined.php

                 Distributed on CD-ROM at GECCO-2009.

                 ACM Order Number 910092.",
}

Genetic Programming entries for Michael D Schmidt Hod Lipson

Citations